To enable a computing device to render a glyph on a display device or a medium, a bitmap that defines each pixel within a shape delineating the glyph may be provided to the computer device as a part of glyph rendering data. A disadvantage of this method is that such a bitmap may require storing or processing a large amount of data. Also, separate bitmaps need to be defined for glyphs at different sizes, even if they are related to the same underlying letter or object.
Instead of using such a brute force approach under which each pixel's color is specified in a bitmap of a glyph, Bézier polygons associated with a functional representation of the glyph's outline as a set of Bézier curves may be used for rendering the glyph. See, e.g., Donald Knuth, Metafont: the Program (Addison-Wesley 1986), pp. 123-131. However, Bézier polygons often overlap with one another, requiring special complicated treatments of pixels that lie simultaneously in multiple Bézier polygons. Additionally, since Bézier polygons are formed by Bézier endpoints that lie on the glyph's outline, and the Bézier polygons are tangent to the outline at these endpoints, the Bézier polygons have vanishing separation from the Bézier curves near the Bézier endpoints, and thus imperfectly support rendering operations such as anti-aliasing operations that need a sufficiently large neighborhood of pixels near the glyph's outline for proper operation. The vanishing separation of Bézier polygons from the curves also tends to exclude many pixels from all the Bézier polygons; thus these points may be missed in anti-aliasing operations that depend on the Bézier polygons, and will be left to uniformly-filled triangles complementing the Bézier polygons, with uneven effects. These problems are worse when a Bézier polygon degenerates into a long narrow straight box.
The approaches described in this section are approaches that could be pursued, but not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the approaches described in this section qualify as prior art merely by virtue of their inclusion in this section. Similarly, issues identified with respect to one or more approaches should not assume to have been recognized in any prior art on the basis of this section, unless otherwise indicated.